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Character Theory of Finite Groups"The book is a pleasure to read. There is no question but that it will become, and deserves to be, a widely used textbook and reference." Bulletin of the American Mathematical Society. Character theory provides a powerful tool for proving theorems about finite groups. In addition to dealing with techniques for applying characters to "pure" group theory, a large part of this book is devoted to the properties of the characters themselves and how these
"The book is a pleasure to read. There is no question but that it will become, and deserves to be, a widely used textbook and reference." -- Bulletin of the American Mathematical Society.Character theory provides a powerful tool for proving theorems about finite groups. In addition to dealing with techniques for applying characters to "pure" group theory, a large part of this book is devoted to the properties of the characters themselves and how these properties reflect and are reflected in the structure of the group.
Chapter I consists of ring theoretic preliminaries. Chapters 2 to 6 and 8 contain the basic material of character theory, while Chapter 7 treats an important technique for the application of characters to group theory. Chapter 9 considers irreducible representations over arbitrary fields, leading to a focus on subfields of the complex numbers in Chapter 10. In Chapter 15 the author introduces Brauer's theory of blocks and "modular characters." Remaining chapters deal with more specialized topics, such as the connections between the set of degrees of the irreducible characters and structure of a group. Following each chapter is a selection of carefully thought out problems, including exercises, examples, further results and extensions and variations of theorems in the text.
Prerequisites for this book are some basic finite group theory: the Sylow theorems, elementary properties of permutation groups and solvable and nilpotent groups. Also useful would be some familiarity with rings and Galois theory. In short, the contents of a first-year graduate algebra course should be sufficient preparation.
Binding Type: Paperback
Publisher: Dover Publications
Published: 11/02/2011
ISBN: 9780486680149
Pages: 336
Weight: 0.76lbs
Size: 8.48h x 5.42w x 0.63d
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★★★★★ 5
Worth the buy
Format: Paperback
Helpful. I prefer this little guy over the gigantic book we were required to purchase along with this one. Barely opened the bigger one, only used this for my advanced assessment course and still got an A.
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Reviewed in the United States on August 23, 2025
★★★★★ 5
A great condition when arrived. Strongly suggested.
Format: Paperback
I love this product and will be a great source for my physical exam study.
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Reviewed in the United States on January 11, 2025
★★★★★ 5
A GREAT PRODUCT
Format: Paperback
very informative and helped me with my class
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Reviewed in the United States on May 15, 2024
★★★★★ 5
Good quality
Format: Paperback
Smaller than the books I'm used to but easy to read.
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Reviewed in the United States on December 8, 2024
★★★★★ 5
Compact handbook
Format: Paperback
This is the perfect pocketbook to tote around to clinicals.
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Reviewed in the United States on June 24, 2023
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